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Satisfaction relations for proper classes: Applications in logic and set theory

Published online by Cambridge University Press:  12 March 2014

Robert A. Van Wesep
Robert A. Van Wesep*
Affiliation:
1402 Bolton Street, Baltimore, MD, 21217, USA, E-mail:rvanwesep@verizon.net
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Abstract

We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate (⊨*) appropriate to such structures. We indicate the utility of this theory as a framework for the development of the metatheory of first-order predicate logic and set theory, and we use it to prove that for any recursively enumerable extension Θ of ZF there is a finitely axiomatizable extension *Θ′ of GB that is a conservative extension of Θ. We also prove a conservative extension result that justifies the use of ⊨* to characterize ground models for forcing constructions.

Keywords

satisfactionproper classclass theoryconservative extensionconservationforcing
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 2 , June 2013 , pp. 345 - 368
Copyright
Copyright © Association for Symbolic Logic 2013

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